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Feedback occurs when outputs of a system are routed back as inputs as part of achain ofcause and effect that forms a circuit or loop.[1] The system can then be said tofeed back into itself. The notion of cause-and-effect has to be handled carefully when applied to feedback systems:
Simple causal reasoning about a feedback system is difficult because the first system influences the second and second system influences the first, leading to a circular argument. This makes reasoning based upon cause and effect tricky, and it is necessary to analyze the system as a whole. As provided by Webster, feedback in business is the transmission of evaluative or corrective information about an action, event, or process to the original or controlling source.[2]
— Karl Johan Åström and Richard M.Murray,Feedback Systems: An Introduction for Scientists and Engineers[3]
Self-regulating mechanisms have existed since antiquity, and the idea of feedback started to entereconomic theory in Britain by the 18th century, but it was not at that time recognized as a universal abstraction and so did not have a name.[4]
The first ever known artificial feedback device was afloat valve, for maintaining water at a constant level, invented in 270 BC inAlexandria, Egypt.[5] This device illustrated the principle of feedback: a low water level opens the valve, the rising water then provides feedback into the system, closing the valve when the required level is reached. This then reoccurs in a circular fashion as the water level fluctuates.[5]
Centrifugal governors were used to regulate the distance and pressure betweenmillstones inwindmills since the 17th century. In 1788,James Watt designed his first centrifugal governor following a suggestion from his business partnerMatthew Boulton, for use in thesteam engines of their production. Early steam engines employed a purelyreciprocating motion, and were used for pumping water – an application that could tolerate variations in the working speed, but the use of steam engines for other applications called for more precise control of the speed.
In1868,James Clerk Maxwell wrote a famous paper, "On governors", that is widely considered a classic in feedback control theory.[6] This was a landmark paper oncontrol theory and the mathematics of feedback.
The verb phraseto feed back, in the sense of returning to an earlier position in a mechanical process, was in use in the US by the 1860s,[7][8] and in 1909, Nobel laureateKarl Ferdinand Braun used the term "feed-back" as a noun to refer to (undesired)coupling between components of anelectronic circuit.[9]
By the end of 1912, researchers using early electronic amplifiers (audions) had discovered that deliberately coupling part of the output signal back to the input circuit would boost the amplification (throughregeneration), but would also cause the audion to howl or sing.[10] This action of feeding back of the signal from output to input gave rise to the use of the term "feedback" as a distinct word by 1920.[10]
The development ofcybernetics from the 1940s onwards was centred around the study of circular causal feedback mechanisms.
Over the years there has been some dispute as to the best definition of feedback. According to cyberneticianAshby (1956), mathematicians and theorists interested in the principles of feedback mechanisms prefer the definition of "circularity of action", which keeps the theory simple and consistent. For those with more practical aims, feedback should be a deliberate effect via some more tangible connection.
[Practical experimenters] object to the mathematician's definition, pointing out that this would force them to say that feedback was present in the ordinary pendulum ... between its position and its momentum—a "feedback" that, from the practical point of view, is somewhat mystical. To this the mathematician retorts that if feedback is to be considered present only when there is an actual wire or nerve to represent it, then the theory becomes chaotic and riddled with irrelevancies.[11]: 54
Focusing on uses in management theory, Ramaprasad (1983) defines feedback generally as "...information about the gap between the actual level and the reference level of a system parameter" that is used to "alter the gap in some way". He emphasizes that the information by itself is not feedback unless translated into action.[12]
Positive feedback: If the signal feedback from output is in phase with the input signal, the feedback is called positive feedback.
Negative feedback: If the signal feedback is out of phase by 180° with respect to the input signal, the feedback is called negative feedback.
As an example of negative feedback, the diagram might represent acruise control system in a car that matches a target speed such as the speed limit. The controlled system is the car; its input includes the combined torque from the engine and from the changing slope of the road (the disturbance). The car's speed (status) is measured by aspeedometer. The error signal is the difference of the speed as measured by the speedometer from the target speed (set point). The controller interprets the speed to adjust the accelerator, commanding the fuel flow to the engine (the effector). The resulting change in engine torque, the feedback, combines with the torque exerted by the change of road grade to reduce the error in speed, minimising the changing slope.
The terms "positive" and "negative" were first applied to feedback prior to WWII. The idea of positive feedback already existed in the 1920s when theregenerative circuit was made.[13] Friis and Jensen (1924) described this circuit in a set of electronic amplifiers as a case wherethe "feed-back" action is positive in contrast to negative feed-back action, which they mentioned only in passing.[14]Harold Stephen Black's classic 1934 paper first details the use of negative feedback in electronic amplifiers. According to Black:
Positive feed-back increases the gain of the amplifier, negative feed-back reduces it.[15]
According to Mindell (2002) confusion in the terms arose shortly after this:
... Friis and Jensen had made the same distinction Black used between "positive feed-back" and "negative feed-back", based not on the sign of the feedback itself but rather on its effect on the amplifier's gain. In contrast, Nyquist and Bode, when they built on Black's work, referred to negative feedback as that with the sign reversed. Black had trouble convincing others of the utility of his invention in part because confusion existed over basic matters of definition.[13]: 121
Even before these terms were being used,James Clerk Maxwell had described their concept through several kinds of "component motions" associated with thecentrifugal governors used in steam engines. He distinguished those that lead to a continuedincrease in a disturbance or the amplitude of a wave or oscillation, from those that lead to adecrease of the same quality.[16]
The terms positive and negative feedback are defined in different ways within different disciplines.
The two definitions may be confusing, like when an incentive (reward) is used to boost poor performance (narrow a gap). Referring to definition 1, some authors use alternative terms, replacingpositive andnegative withself-reinforcing andself-correcting,[18]reinforcing andbalancing,[19]discrepancy-enhancing anddiscrepancy-reducing[20] orregenerative anddegenerative[21] respectively. And for definition 2, some authors promote describing the action or effect aspositive andnegativereinforcement orpunishment rather than feedback.[12][22]Yet even within a single discipline an example of feedback can be called either positive or negative, depending on how values are measured or referenced.[23]
This confusion may arise because feedback can be used to provideinformation ormotivate, and often has both aqualitative and aquantitative component. As Connellan and Zemke (1993) put it:
Quantitative feedback tells us how much and how many.Qualitative feedback tells us how good, bad or indifferent.[24]: 102
While simple systems can sometimes be described as one or the other type, many systems with feedback loops cannot be shoehorned into either type, and this is especially true when multiple loops are present.
When there are only two parts joined so that each affects the other, the properties of the feedback give important and useful information about the properties of the whole. But when the parts rise to even as few as four, if every one affects the other three, then twenty circuits can be traced through them; and knowing the properties of all the twenty circuits does not give complete information about the system.[11]: 54
In general, feedback systems can have many signals fed back and the feedback loop frequently contain mixtures of positive and negative feedback where positive and negative feedback can dominate at different frequencies or different points in the state space of a system.
The term bipolar feedback has been coined to refer to biological systems where positive and negative feedback systems can interact, the output of one affecting the input of another, and vice versa.[25]
Some systems with feedback can have very complex behaviors such aschaotic behaviors in non-linear systems, while others have much more predictable behaviors, such as those that are used to make and design digital systems.
Feedback is used extensively in digital systems. For example, binary counters and similar devices employ feedback where the current state and inputs are used to calculate a new state which is then fed back and clocked back into the device to update it.
By using feedback properties, the behavior of a system can be altered to meet the needs of an application; systems can be made stable, responsive or held constant. It is shown that dynamical systems with a feedback experience an adaptation to theedge of chaos.[26]
Physical systems present feedback through the mutual interactions of its parts. Feedback is also relevant for the regulation of experimental conditions, noise reduction, and signal control.[27] The thermodynamics of feedback-controlled systems has intrigued physicist since theMaxwell's demon, with recent advances on the consequences for entropy reduction and performance increase.[28][29]
Inbiological systems such asorganisms,ecosystems, or thebiosphere, most parameters must stay under control within a narrow range around a certain optimal level under certain environmental conditions. The deviation of the optimal value of the controlled parameter can result from the changes in internal and external environments. A change of some of the environmental conditions may also require change of that range to change for the system to function. The value of the parameter to maintain is recorded by a reception system and conveyed to a regulation module via an information channel. An example of this isinsulin oscillations.
Biological systems contain many types of regulatory circuits, both positive and negative. As in other contexts,positive andnegative do not imply that the feedback causesgood orbad effects. A negative feedback loop is one that tends to slow down a process, whereas the positive feedback loop tends to accelerate it. Themirror neurons are part of a social feedback system, when an observed action is "mirrored" by the brain—like a self-performed action.
Normal tissue integrity is preserved by feedback interactions between diverse cell types mediated by adhesion molecules and secreted molecules that act as mediators; failure of key feedback mechanisms in cancer disrupts tissue function.[30]In an injured or infected tissue, inflammatory mediators elicit feedback responses in cells, which alter gene expression, and change the groups of molecules expressed and secreted, including molecules that induce diverse cells to cooperate and restore tissue structure and function. This type of feedback is important because it enables coordination of immune responses and recovery from infections and injuries. During cancer, key elements of this feedback fail. This disrupts tissue function and immunity.[31][32]
Mechanisms of feedback were first elucidated in bacteria, where a nutrient elicits changes in some of their metabolic functions.[33]Feedback is also central to the operations ofgenes andgene regulatory networks.Repressor (seeLac repressor) andactivatorproteins are used to create geneticoperons, which were identified byFrançois Jacob andJacques Monod in 1961 asfeedback loops.[34] These feedback loops may be positive (as in the case of the coupling between a sugar molecule and the proteins that import sugar into a bacterial cell), or negative (as is often the case inmetabolic consumption).
On a larger scale, feedback can have a stabilizing effect on animal populations even when profoundly affected by external changes, although time lags in feedback response can give rise topredator-prey cycles.[35]
Inzymology, feedback serves as regulation of activity of an enzyme by its direct product(s) or downstream metabolite(s) in the metabolic pathway (seeAllosteric regulation).
Thehypothalamic–pituitary–adrenal axis is largely controlled by positive and negative feedback, much of which is still unknown.
Inpsychology, the body receives a stimulus from the environment or internally that causes the release ofhormones. Release of hormones then may cause more of those hormones to be released, causing a positive feedback loop. This cycle is also found in certain behaviour. For example, "shame loops" occur in people who blush easily. When they realize that they are blushing, they become even more embarrassed, which leads to further blushing, and so on.[36]
The climate system is characterized by strong positive and negative feedback loops between processes that affect the state of the atmosphere, ocean, and land. A simple example is theice–albedo positive feedback loop whereby melting snow exposes more dark ground (of loweralbedo), which in turn absorbs heat and causes more snow to melt.
Feedback is extensively used in control theory, using a variety of methods includingstate space (controls),full state feedback, and so forth. In the context of control theory, "feedback" is traditionally assumed to specify "negative feedback".[39]
The most common general-purposecontroller using a control-loop feedback mechanism is aproportional-integral-derivative (PID) controller. Heuristically, the terms of a PID controller can be interpreted as corresponding to time: the proportional term depends on thepresent error, the integral term on the accumulation ofpast errors, and the derivative term is a prediction offuture error, based on current rate of change.[40]
For feedback in the educational context, seecorrective feedback.
In ancient times, thefloat valve was used to regulate the flow of water in Greek and Romanwater clocks; similar float valves are used to regulate fuel in acarburettor and also used to regulate tank water level in theflush toilet.
The Dutch inventorCornelius Drebbel (1572–1633) built thermostats (c1620) to control the temperature of chicken incubators and chemical furnaces. In 1745, the windmill was improved by blacksmith Edmund Lee, who added afantail to keep the face of the windmill pointing into the wind. In 1787,Tom Mead regulated the rotation speed of a windmill by using acentrifugal pendulum to adjust the distance between the bedstone and the runner stone (i.e., to adjust the load).
The use of thecentrifugal governor byJames Watt in 1788 to regulate the speed of hissteam engine was one factor leading to theIndustrial Revolution. Steam engines also use float valves andpressure release valves as mechanical regulation devices. Amathematical analysis of Watt's governor was done byJames Clerk Maxwell in 1868.[16]
TheGreat Eastern was one of the largest steamships of its time and employed a steam powered rudder with feedback mechanism designed in 1866 byJohn McFarlane Gray.Joseph Farcot coined the wordservo in 1873 to describe steam-powered steering systems. Hydraulic servos were later used to position guns.Elmer Ambrose Sperry of theSperry Corporation designed the firstautopilot in 1912.Nicolas Minorsky published a theoretical analysis of automatic ship steering in 1922 and described thePID controller.[41]
Internal combustion engines of the late 20th century employed mechanical feedback mechanisms such as thevacuum timing advance but mechanical feedback was replaced by electronicengine management systems once small, robust and powerful single-chipmicrocontrollers became affordable.
The use of feedback is widespread in the design ofelectronic components such asamplifiers,oscillators, and statefullogic circuit elements such asflip-flops andcounters. Electronic feedback systems are also very commonly used to control mechanical, thermal and other physical processes.
If the signal is inverted on its way round the control loop, the system is said to havenegative feedback;[43] otherwise, the feedback is said to bepositive. Negative feedback is often deliberately introduced to increase thestability and accuracy of a system by correcting or reducing the influence of unwanted changes. This scheme can fail if the input changes faster than the system can respond to it. When this happens, the lag in arrival of the correcting signal can result in over-correction, causing the output tooscillate or "hunt".[44] While often an unwanted consequence of system behaviour, this effect is used deliberately in electronic oscillators.
Harry Nyquist atBell Labs derived theNyquist stability criterion for determining the stability of feedback systems. An easier method, but less general, is to useBode plots developed byHendrik Bode to determine thegain margin and phase margin. Design to ensure stability often involvesfrequency compensation to control the location of thepoles of the amplifier.
Electronic feedback loops are used to control the output ofelectronic devices, such asamplifiers. A feedback loop is created when all or some portion of the output is fed back to the input. A device is said to be operatingopen loop if no output feedback is being employed andclosed loop if feedback is being used.[45]
When two or more amplifiers are cross-coupled using positive feedback, complex behaviors can be created. Thesemultivibrators are widely used and include:
Negative feedback occurs when the fed-back output signal has a relative phase of 180° with respect to the input signal (upside down). This situation is sometimes referred to as beingout of phase, but that term also is used to indicate other phase separations, as in "90° out of phase". Negative feedback can be used to correct output errors or to desensitize a system to unwanted fluctuations.[46] In feedback amplifiers, this correction is generally for waveformdistortion reduction[47] or to establish a specifiedgain level. A general expression for the gain of a negative feedback amplifier is theasymptotic gain model.
Positive feedback occurs when the fed-back signal is in phase with the input signal. Under certain gain conditions, positive feedback reinforces the input signal to the point where the output of the deviceoscillates between its maximum and minimum possible states. Positive feedback may also introducehysteresis into a circuit. This can cause the circuit to ignore small signals and respond only to large ones. It is sometimes used to eliminate noise from a digital signal. Under some circumstances, positive feedback may cause a device to latch, i.e., to reach a condition in which the output is locked to its maximum or minimum state. This fact is very widely used in digital electronics to makebistable circuits for volatile storage of information.
The loud squeals that sometimes occurs insound reinforcement,public address systems, androck music are known asaudio feedback. If a microphone is in front of a loudspeaker that it is connected to, sound that the microphone picks up comes out of the speaker, and is picked up by the microphone and re-amplified. If theloop gain is sufficient, howling or squealing at the maximum power of the amplifier is possible.
Anelectronic oscillator is anelectronic circuit that produces a periodic,oscillating electronic signal, often asine wave or asquare wave.[48][49] Oscillators convertdirect current (DC) from a power supply to analternating current signal. They are widely used in many electronic devices. Common examples of signals generated by oscillators include signals broadcast byradio andtelevision transmitters, clock signals that regulate computers andquartz clocks, and the sounds produced by electronic beepers andvideo games.[48]
Oscillators are often characterized by thefrequency of their output signal:
Oscillators designed to produce a high-power AC output from a DC supply are usually calledinverters.
There are two main types of electronic oscillator: the linear or harmonic oscillator and the nonlinear orrelaxation oscillator.[49][50]
A latch or aflip-flop is acircuit that has two stable states and can be used to store state information. They typically constructed using feedback that crosses over between two arms of the circuit, to provide the circuit with a state. The circuit can be made to change state by signals applied to one or more control inputs and will have one or two outputs. It is the basic storage element insequential logic. Latches and flip-flops are fundamental building blocks ofdigital electronics systems used in computers, communications, and many other types of systems.
Latches and flip-flops are used as data storage elements. Such data storage can be used for storage ofstate, and such a circuit is described assequential logic. When used in afinite-state machine, the output and next state depend not only on its current input, but also on its current state (and hence, previous inputs). It can also be used for counting of pulses, and for synchronizing variably-timed input signals to some reference timing signal.
Flip-flops can be either simple (transparent or opaque) orclocked (synchronous or edge-triggered). Although the term flip-flop has historically referred generically to both simple and clocked circuits, in modern usage it is common to reserve the termflip-flop exclusively for discussing clocked circuits; the simple ones are commonly calledlatches.[51][52]
Using this terminology, a latch is level-sensitive, whereas a flip-flop is edge-sensitive. That is, when a latch is enabled it becomes transparent, while a flip flop's output only changes on a single type (positive going or negative going) of clock edge.
Feedback loops provide generic mechanisms for controlling the running, maintenance, and evolution of software and computing systems.[53] Feedback-loops are important models in the engineering of adaptive software, as they define the behaviour of the interactions among the control elements over the adaptation process, to guarantee system properties at run-time. Feedback loops and foundations of control theory have been successfully applied to computing systems.[54] In particular, they have been applied to the development of products such asIBM Db2 andIBM Tivoli. From a software perspective, theautonomic (MAPE, monitor analyze plan execute) loop proposed by researchers of IBM is another valuable contribution to the application of feedback loops to the control of dynamic properties and the design and evolution of autonomic software systems.[55][56]
Feedback is also a useful design principle for designinguser interfaces.
Video feedback is thevideo equivalent ofacoustic feedback. It involves a loop between avideo camera input and a video output, e.g., atelevision screen ormonitor. Aiming the camera at the display produces a complex video image based on the feedback.[57]
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This chapter describescausal loop diagrams to portray the information feedback at work in a system. The wordcausal refers to cause-and-effect relationships. The wordloop refers to a closed chain of cause and effect that creates the feedback.
[In a practical amplifier] the forward path may not be strictly unilateral, the feedback path is usually bilateral, and the input and output coupling networks are often complicated.
If the feedback signal reduces the input signal,i.e. it is out of phase with the input [signal], it is called negative feedback.
The parameters of a system ... may vary... The primary advantage of using feedback in control systems is to reduce the system's sensitivity to parameter variations.
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